In SEM, EPMA, microfocus X-ray tube and other electron beam-employing devices which utilize an electron microprobe, focusing as large a beam current as possible on the observed sample (X-ray target) with as small a probe diameter as possible is important for increasing the S/N (signal to noise) ratio and resolution. FIG. 8 shows the lens configuration of an electron probe-forming system using a Schottky emitter. In the electron gun, an extraction electrode 12 and acceleration electrode 13 are arranged between an emitter 11 and a condenser lens 14, and a suppressor electrode (not illustrated) is arranged sandwiching the emitter 11 on the side opposite to that of the extraction electrode 12. The electron beam from the emitter 11 is controlled by the condenser lens 14, and the desired beam current is extracted using an aperture 15a placed inside diaphragm lens 15. After passing the aperture, the electron beam forms an electron probe focused on the sample (target) 17 using the diaphragm lens 15 and objective lens 16.
An important matter in forming a probe which is as small as possible at a given beam current is to focus the beam on the sample 17 at the optimal aperture angle α opt for the beam current Ib. This will be explained using formulas. The probe diameter of the electron beam obtained on the sample 17 is determined by the contributions of the electron source's Gaussian image diameter, diffraction aberration, spherical aberration and chromatic aberration. The probe diameter is generally given by the following formula.
                                          d            2                    =                                    Pα              6                        +                          Q              ⁢                                                          ⁢                              α                2                                      +            R            +                          S                              α                2                                                    ⁢                                  ⁢                  P          =                                    1              8                        ⁢                          C              s              2                                      ⁢                                  ⁢                  Q          =                                                    1                2                            ⁢                                                                    C                    s                    2                                    ⁡                                      (                                                                  Δ                        ⁢                                                                                                  ⁢                        E                                                                    V                        acc                                                              )                                                  2                                      +                                          4                                  π                  4                                            ⁢                              C                s                            ⁢                                                                    C                    sg                                    ⁡                                      (                                                                  V                        acc                                                                    V                        ext                                                              )                                                                    3                  /                  2                                            ⁢                                                (                                                            I                      b                                        B                                    )                                2                            ⁢                              1                                  d                  co                  4                                                                    ⁢                                  ⁢                  R          =                                    4                              π                2                                      ⁢                          C              c                        ⁢                                                            C                  cg                                ⁡                                  (                                                            Δ                      ⁢                                                                                          ⁢                      E                                                              V                      acc                                                        )                                            2                        ⁢                                          (                                                      V                    acc                                                        V                    ext                                                  )                                            3                /                2                                      ⁢                                          I                b                            B                        ⁢                          1                              d                co                2                                                    ⁢                                  ⁢                  S          =                                                    4                                  π                  2                                            ⁢                                                I                  b                                B                                      +                                                            (                                      1.22                    ⁢                                                                                  ⁢                    λ                                    )                                2                            2                        +                                          32                                  π                  2                                            ⁢                                                                    C                    cg                    2                                    ⁡                                      (                                                                  V                        acc                                                                    V                        ext                                                              )                                                  2                            ⁢                                                (                                                            I                      b                                        B                                    )                                4                            ⁢                              1                                  d                  co                  4                                                      +                                          8                                  π                  4                                            ⁢                                                                    C                    cg                    2                                    ⁡                                      (                                                                  Δ                        ⁢                                                                                                  ⁢                        E                                                                    V                        acc                                                              )                                                  2                            ⁢                                                (                                                            V                      acc                                                              V                      ext                                                        )                                3                            ⁢                                                (                                                            I                      b                                        B                                    )                                2                            ⁢                              1                                  d                  co                  4                                                                                        (        1        )            
Here, Cs and Cc are the spherical and chromatic aberration coefficients of the objective lens, Vext and Vacc are the extraction and acceleration voltages of the electron gun, ΔE is the beam energy spread, Csg and Ccg are the spherical and chromatic aberration coefficients of the condenser lens, B is the electron beam brightness, and dco represents the diameter of the electron source. λ is the de Broglie wavelength of electrons. Formula (1) is a form of a previously known probe diameter evaluation formula extended to take into account the aberration of the electron gun section and condenser lens section. When an electron gun with a low angular current density, such as a field emission type emitter, is used as the electron source, if only the objective lens aberration is taken into account, the evaluation of probe diameter becomes inaccurate and use of formula (1) is essential.
The various coefficients of formula (1) are determined when the desired beam current Ib has been given, so there exists an aperture angle which minimizes the probe diameter d, i.e. an optimal aperture angle α opt, expressed by the following formula (2).
                              α          opt          4                =                                                                              Q                  2                                +                                  12                  ⁢                                                                          ⁢                  PS                                                      -            Q                                6            ⁢            P                                              (        2        )            It is desirable to adjust the beam aperture angle on the sample in accordance with the beam current value to the value given by formula (2).
The optical parameter of lens system total magnification ratio M (ratio between the Gaussian image diameter dg on the sample and the electron source diameter dco) is introduced in order to achieve the optimal aperture angle α opt. The total magnification ratio M can be computed based on focal distance of the lenses once their excitation intensities have been determined. Furthermore, the following relational expression obtains between the ratio between beam current and brightness (Ib/B) and the total magnification ratio M.
                    M        =                              2            π                    ⁢                      1                          d              co                                ⁢                                                    I                b                            B                                ⁢                      1                          α              opt                                                          (        3        )            
The dependence of optimal aperture angle α opt on beam current is always there in the form of a ratio to brightness, (Ib/B), so if the parameter t=Ib/B is defined, the total magnification ratio M and the aperture angle α opt can both be expressed as a function of t.M=M(t) αopt=αopt(t)  (41)
Optimal aperture angle control can thus be achieved if the combination of total magnification ratio and optimal aperture angle (M, α opt) moves along the ideal “operating curve” given by formula (4) when the beam current is changed. “Lens system total magnification ratio” and “beam aperture angle” are both operating parameters which can be unambiguously calculated based on lens arrangement and lens strengths, making it possible to place the beam conditions on the operating curve without dependency on parameters that depend on the operating state of the electron gun, such as beam current and beam brightness, which were necessary in the prior art.
FIG. 2 shows an example of the determination of operating curve (M, α opt) for the system shown in FIG. 8. It can be seen that the beam aperture angle α opt should be constant in the region where beam current Ib is small and should increase proportionally to about the (⅓) power of total magnification ratio M in the middle region. In the large beam current region, it is necessary to increase the current by increasing the beam aperture angle α opt while keeping the total magnification ratio M constant. The total magnification ratio M in the large beam current region where total magnification ratio M becomes constant is referred to as asymptotic total magnification ratio Masymp. Using the parameters appearing in formula (1), this asymptotic total magnification ratio Masymp is given by the following (see Non-patent literature 1):Mamp=1.3161(Vext/Vacc)3/8(Cs/Csg)1/4  (5)
FIG. 3 shows an example of evaluation in which the probe property (relationship between beam current Ib and probe diameter d on the sample) has been determined for when the excitation conditions of the lens system correspond to the operating curve, i.e. when an optimal beam aperture angle has been achieved. The figure illustrates the typical probe property when using a Schottky emitter electron gun, which is one kind of field emission type emitter, and shows that the probe diameter is essentially constant regardless of current when the beam current is small, increases gradually with current in the middle region, and increases sharply at d∝Ib3/2 when a certain beam current threshold is exceeded. This corresponds to how the control of the optimal aperture angle α opt shown in FIG. 2 differs according to the beam current region (see Patent literature 1).